Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers

被引：48

作者：

Li, Weigu ^{[1
]}

Llibre, Jaume ^{[2
]}

Yang, Jiazhong ^{[1
]}

Zhang, Zhifen ^{[1
]}

机构：

[1] Peking Univ, Dept Math, Beijing 100871, Peoples R China

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2009年 / 21卷 / 01期

关键词：

Homogeneous centers; Quasi-homogeneous centers; Limit cycles; QUADRATIC HAMILTONIAN-SYSTEMS; COMPLETE ABELIAN-INTEGRALS; HILBERTS 16TH PROBLEM; VECTOR-FIELDS; POLYNOMIAL PERTURBATIONS; EXPONENTIAL ESTIMATE; ISOCHRONOUS CENTERS; ELLIPTIC INTEGRALS; LINEAR ESTIMATE; ALMOST-ALL;

D O I：

10.1007/s10884-008-9126-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of any homogeneous and quasi-homogeneous center, which can be obtained using the Abelian integral method of first order. We show that these bounds are the best possible using the Abelian integral method of first order. We note that these centers are in general non-Hamiltonian. As a consequence of our study we provide the biggest known number of limit cycles surrounding a unique singular point in terms of the degree n of the system for arbitrary large n.

引用

页码：133 / 152

页数：20

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